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\[\cos(x+y)=x\]
\[\cos^{-1} x=x+y\]
\[y=\cos^{-1} x-x\]
\[dy/dx=(\cos^{-1} x-x)\prime\]

\[dy/dx=-1/\sqrt{1-x^2}-1\]

i hope i am not doing any mistake...

if this is right, fan me plz.

yeah probably.